Numerical Solution of the Burgers' Equation Based on Sinc Method

محورهای موضوعی : Applied Mathematics

Ghasem Kazemi Gelian ¹ ( Department of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, Iran )
Mohammad Ali Fariborzi Araghi ² ( Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. )

تاریخ دریافت : 1397/09/14 تاریخ پذیرش : 1397/12/13 تاریخ انتشار : 1398/02/11

کلید واژه: ‎Single‎ ‎Exponential Transformation, Burgers' Equation‎, ‎Sinc method‎,

چکیده مقاله :

Burgers' equation arises in various areas of applied mathematics,‎‎such as modeling of dynamics‎, ‎heat conduction‎, ‎and acoustic‎‎waves‎ Also‎, ‎this equation has a large variety of applications in‎‎the modeling of water in unsaturated soil‎, ‎dynamics of soil‎‎water‎, ‎models of traffic‎, ‎turbulence and fluid flow‎, ‎mixing and‎‎turbulent diffusion. Many researchers tried to find analytic and numerical solutions of‎‎ this equation by different methods.Sinc method is a powerful numerical tool for finding fast and‎‎accurate solution in various areas of problems.‎In this paper‎, ‎numerical solution of Burgers' equation‎‎is considered by applying Sinc method‎. ‎For this purpose‎, ‎we apply‎‎Sinc method in cooperative with a classic finite difference‎‎formula to‎ ‎Burgers'equation‎. ‎‎The purpose of this paper is to extend the application of the‎‎sinc method for solving Burgers'equation by considering stability‎‎analysis of the method.‎ Numerical examples are provided to verify the validity of proposed method

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